CHAPTER 5: MAGNETISM AND MATTER
SAMPLE QUESTION PAPER (ASSIGNMENT-1)
- There are 33 questions in all. All questions are compulsory.
- Section A: 16 questions (12 MCQs and 4 Assertion-Reasoning) of 1 mark each.
- Section B: 5 short answer questions of 2 marks each.
- Section C: 7 short answer questions of 3 marks each.
- Section D: 2 case study-based questions of 4 marks each.
- Section E: 3 long answer questions of 5 marks each.
SECTION A (16 Marks)
Q.1. Gauss's law in magnetism, $\displaystyle {\oint \vec{B} \cdot d\vec{A} = 0}$ over any closed surface, is a direct consequence of:
Explanation: Magnetic field lines always form continuous closed loops without beginning or end, so net magnetic flux entering any closed surface equals net flux leaving it.
Q.2. At a place, the horizontal component of the earth's magnetic field $\displaystyle {B_H}$ is $\displaystyle {\sqrt{3}}$ times the vertical component $\displaystyle {B_V}$. The angle of dip $\displaystyle {\delta}$ at that place is:
Explanation: $\displaystyle {\tan\delta = {\frac{{B_V}}{{B_H}}} = {\frac{{B_V}}{{\sqrt{3} B_V}}} = {\frac{{1}}{{\sqrt{3}}}} \implies \delta = 30^\circ}$.
Q.3. According to Curie's law, the magnetic susceptibility $\displaystyle {\chi}$ of a paramagnetic substance at absolute temperature $\displaystyle {T}$ is proportional to:
Explanation: Curie's law states $\displaystyle {\chi = C/T}$, so susceptibility is inversely proportional to absolute temperature $\displaystyle {T}$.
Q.4. A bar magnet of magnetic moment $\displaystyle {M}$ is cut into two equal halves breadth-wise (perpendicular to its length). The magnetic moment of each half becomes:
Explanation: Pole strength $\displaystyle {m}$ remains unchanged, but length is halved ($\displaystyle {l' = l/2}$), so $\displaystyle {M' = m (2l') = m l = M/2}$.
Q.5. The Curie temperature is the temperature above which:
Explanation: Above Curie temperature $\displaystyle {T_C}$, thermal agitation destroys domain alignment in ferromagnetic materials, turning them paramagnetic.
Q.6. The magnetic susceptibility $\displaystyle {\chi}$ of diamagnetic substances is:
Explanation: Diamagnetic materials get weakly magnetised in a direction opposite to applied field, giving a small negative value of $\displaystyle {\chi}$.
Q.7. A material suitable for making permanent magnets should possess:
Explanation: Permanent magnets must retain strong residual magnetism (high retentivity) and resist stray demagnetising fields (high coercivity).
Q.8. A dip needle, free to rotate in a vertical plane, sets itself vertical at a certain place on the earth. The angle of dip at this place is:
Explanation: At the magnetic poles of the earth, horizontal component $\displaystyle {B_H = 0}$, so the field is entirely vertical ($\displaystyle {\delta = 90^\circ}$).
Directions for Q.13 to Q.16:
(a) Both Assertion and Reason are true and Reason is correct explanation.
(b) Both Assertion and Reason are true but Reason is NOT correct explanation.
(c) Assertion is true but Reason is false.
(d) Both Assertion and Reason are false.
Q.13. Assertion (A): A bar magnet held in a uniform magnetic field experiences no net force, but it may experience a torque.
Reason (R): The two equal and opposite forces acting on the poles of the magnet act along different lines, forming a couple.
Explanation: Equal opposite forces $\displaystyle {m B}$ and $\displaystyle {-m B}$ cancel for net translation ($\displaystyle {F_{\text{net}} = 0}$), but form a couple producing torque $\displaystyle {\tau = M B \sin\theta}$.
Q.14. Assertion (A): Soft iron is preferred over steel for making electromagnet cores and transformer cores.
Reason (R): Soft iron has high permeability together with low retentivity and low coercivity, so it magnetises and demagnetises easily with small hysteresis loss.
Q.15. Assertion (A): A paramagnetic sample, when placed in a non-uniform magnetic field, tends to move from weaker field to stronger field regions.
Reason (R): Paramagnetic materials get weakly magnetised in the direction of the applied magnetic field.
Q.16. Assertion (A): Magnetic field lines never intersect each other.
Reason (R): If two field lines intersected, the magnetic field would have two different directions at the point of intersection, which is physically impossible.
SECTION B (10 Marks)
Q.17. Distinguish between diamagnetic and paramagnetic substances on the basis of (i) susceptibility $\displaystyle {\chi}$, (ii) behavior in a non-uniform magnetic field.
(i) Susceptibility: Diamagnetic $\displaystyle {\chi}$ is small and negative ($\displaystyle {-1 \le \chi < 0}$); Paramagnetic $\displaystyle {\chi}$ is small and positive ($\displaystyle {0 < \chi < \varepsilon}$).
(ii) Non-uniform Field: Diamagnetic tends to move from stronger to weaker field regions; Paramagnetic tends to move from weaker to stronger field regions.
Q.18. A compass needle of magnetic moment $\displaystyle {60\text{ A}\cdot\text{m}^2}$ experiencing a torque of $\displaystyle {1.2 \times 10^{-3}\text{ N}\cdot\text{m}}$ when aligned at $\displaystyle {30^\circ}$ to a uniform magnetic field. Calculate the magnitude of magnetic field $\displaystyle {B}$.
$\displaystyle {B = {\frac{{1.2 \times 10^{-3}}}{{60 \times \sin 30^\circ}}} = {\frac{{1.2 \times 10^{-3}}}{{60 \times 0.5}}} = {\frac{{1.2 \times 10^{-3}}}{{30}}} = 4 \times 10^{-5}\text{ T}}$.
Q.19. State Gauss's Law in magnetism. What is its fundamental physical significance regarding magnetic poles?
Significance: It proves that isolated magnetic monopoles do not exist in nature; magnetic poles always exist in equal and opposite N-S pairs.
Q.20. At a certain location, horizontal component of earth's magnetic field is $\displaystyle {0.3\text{ G}}$ and angle of dip is $\displaystyle {60^\circ}$. Find total intensity of earth's magnetic field $\displaystyle {B}$ and vertical component $\displaystyle {B_V}$.
Vertical component: $\displaystyle {B_V = B \sin 60^\circ = 0.6 \times {\frac{{\sqrt{3}}}{{2}}} = 0.3\sqrt{3}\text{ G} \approx 0.52\text{ G}}$.
ASSIGNMENT – 2 (MCQ PRACTICE)
1. According to Curie's law, the magnetic susceptibility ($\displaystyle {\chi}$) of a paramagnetic substance at absolute temperature $\displaystyle {T}$ is proportional to:
Explanation: Curie's Law $\displaystyle {\chi = C/T}$, so $\displaystyle {\chi \propto 1/T}$.
2. At a place, horizontal component of earth's magnetic field is $\displaystyle {\sqrt{3}}$ times the vertical component. Angle of dip is:
Explanation: $\displaystyle {\tan\delta = B_V/B_H = 1/\sqrt{3} \implies \delta = 30^\circ}$.
3. Which statement about magnetic field lines is NOT correct?
Explanation: Inside a magnet, field lines run from South pole to North pole to form continuous closed loops.
4. A dip needle free to rotate in a vertical plane sets itself vertical at a certain place on earth. Angle of dip is:
Explanation: Occurs at the magnetic poles of the earth.
5. Relative magnetic permeability ($\displaystyle {\mu_r}$) of a ferromagnetic material is:
Explanation: Ferromagnetics have very large positive permeability ($\displaystyle {\mu_r \sim 10^3 - 10^5}$).
6. The Curie temperature is the temperature above which:
Explanation: Thermal agitation destroys domain alignment above $\displaystyle {T_C}$.
7. A material suitable for making permanent magnets should have:
8. A bar magnet of magnetic moment $\displaystyle {M}$ is cut into two equal halves breadth-wise. Magnetic moment of each half becomes:
9. Gauss's law in magnetism, $\displaystyle {\oint \vec{B}\cdot d\vec{A} = 0}$, is a direct consequence of:
10. Magnetic susceptibility of diamagnetic substances is:
ASSIGNMENT – 3 (ASSERTION & REASON)
1. Assertion (A): A bar magnet held in a uniform magnetic field experiences no net force, but it may experience a torque.
Reason (R): The two equal and opposite forces acting on the poles of the magnet act along different lines, forming a couple.
2. Assertion (A): Soft iron is preferred over steel for making electromagnet cores.
Reason (R): Soft iron has high permeability together with low retentivity and low coercivity, so it magnetises and demagnetises easily.
3. Assertion (A): A paramagnetic sample, when placed in a non-uniform magnetic field, tends to move towards the region of stronger field.
Reason (R): Paramagnetic materials get weakly magnetised in the direction of the applied field.
4. Assertion (A): Magnetic field lines never intersect each other.
Reason (R): If two field lines intersected, the magnetic field would have two different directions at the point of intersection, which is not possible.
5. Assertion (A): Diamagnetism is present in every material, even those that are ultimately paramagnetic or ferromagnetic.
Reason (R): Diamagnetism arises from orbital motion of electrons, developing induced magnetic moment opposing applied field.
Explanation: In paramagnetic/ferromagnetic materials, strong paramagnetic alignment masks the weak fundamental diamagnetic effect.
ASSIGNMENT – 4 (COMPETENCY BASED QUESTIONS)
Case Study 1: Elements of Earth's Magnetic Field
Earth's magnetic field is characterized by magnetic declination, angle of dip ($\displaystyle {\delta}$), and horizontal component ($\displaystyle {B_H = B \cos\delta}$).
(i) Relation between components: (a) $\displaystyle {B_V = B_H \tan\delta}$ (b) $\displaystyle {B_H = B_V \tan\delta}$
(ii) At magnetic poles, freely suspended compass needle: (a) Points horizontally (b) Becomes vertical
(iii) Angle of dip is $\displaystyle {90^\circ}$ at: (a) Magnetic equator (b) Magnetic pole
Case Study 2: Hysteresis and Choice of Magnetic Materials
The lagging of magnetic induction $\displaystyle {B}$ behind magnetising field $\displaystyle {H}$ in ferromagnetic materials is called hysteresis.
(i) Area enclosed by hysteresis loop represents: (a) Retentivity (b) Energy loss per cycle per unit volume
(ii) Material best suited for transformer cores: (a) Steel (b) Soft iron
(iii) Material with broad hysteresis loop suited for: (a) Permanent magnets (b) Transformer cores
Case Study 3: Bar Magnet as an Equivalent Dipole
A bar magnet of moment $\displaystyle {M}$ produces fields on axial and equatorial lines.
(i) Axial field at distance $\displaystyle {r}$ ($\displaystyle {r \gg l}$): (a) $\displaystyle {\mu_0 M / 4\pi r^3}$ (b) $\displaystyle {2\mu_0 M / 4\pi r^3}$
(ii) Potential energy of dipole at angle $\displaystyle {\theta}$: (a) $\displaystyle {-M B \cos\theta}$ (b) $\displaystyle {M B \sin\theta}$
(iii) Work done rotating dipole from stable ($\displaystyle {0^\circ}$) to unstable ($\displaystyle {180^\circ}$) equilibrium: (a) $\displaystyle {M B}$ (b) $\displaystyle {2 M B}$
ASSIGNMENT – 5 (FORMULAE & CONCEPTUAL QUESTIONS)
CORE FORMULAE SUMMARY
Axial Line: $\displaystyle {B_{\text{axial}} = {\frac{{\mu_0}}{{4\pi}}} {\frac{{2M}}{{r^3}}}}$ | Equatorial Line: $\displaystyle {B_{\text{equatorial}} = {\frac{{\mu_0}}{{4\pi}}} {\frac{{M}}{{r^3}}}}$
Torque: $\displaystyle {\vec{\tau} = \vec{M} \times \vec{B} \implies \tau = M B \sin\theta}$ | Potential Energy: $\displaystyle {U = -\vec{M} \cdot \vec{B} = -M B \cos\theta}$
$\displaystyle {\chi = {\frac{{M}}{{H}}}}$, $\displaystyle {\mu_r = 1 + \chi}$, $\displaystyle {B = \mu H = \mu_0 \mu_r H}$
Curie's Law: $\displaystyle {\chi = {\frac{{C}}{{T}}}}$ | Earth Field: $\displaystyle {B_H = B \cos\delta, B_V = B \sin\delta, \tan\delta = {\frac{{B_V}}{{B_H}}}}$
CONCEPTUAL QUESTIONS
1. Why do magnetic field lines form continuous closed loops whereas electric field lines do not?
2. How does temperature affect the susceptibility of (i) diamagnetic, (ii) paramagnetic, (iii) ferromagnetic materials?
(i) Diamagnetic: Susceptibility $\displaystyle {\chi}$ is independent of temperature.
(ii) Paramagnetic: Susceptibility decreases inversely with temperature ($\displaystyle {\chi \propto 1/T}$).
(iii) Ferromagnetic: Decreases slowly with temperature; above Curie temperature $\displaystyle {T_C}$, it transforms into a paramagnetic material following Curie-Weiss law $\displaystyle {\chi = C / (T - T_C)}$.
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